According you and your dentist; your mother may be suffering from periodontitis. In this problem; swollen gums, bleeding on brushing, sensitivity problem, receding gums, mobility in teeth-
all the above symptoms may cause pain in teeth, if many teeth involved then generalized jaw pain may occurs.
In above symptoms, generalized bone loss and prognosis is poor. First scaling and root planning with medicines. If possible then bone grafting. But if patient not maintaining oral hygiene then situation will be more worst in future. So keep maintaining oral hygiene.
Next Steps
please consult periodontics (gums specialist)
Health Tips
warm saline rinses for every 2 hours is helpful for your problem.